01Workspace

Notebooks

Ideas, taken apart

Notebooks is the workspace folder for taking something apart in public.

A notebook assumes almost nothing and hides almost nothing. It starts from a picture you already have, adds one idea at a time, and draws every idea that can be drawn. The figures are not decoration. They are the argument, and most of them are yours to push on.

Nothing here is a summary of an explanation that lives somewhere else. If I could not build the intuition from the ground, I did not publish it.

indexnotebooks

00August 2026ten-off-the-shelfTen Off the ShelfOn 1 August 2026 OpenAI published 249 pages settling ten open problems, with no human author named anywhere in it. Ten problems came off a shelf that took sixty-two years to build: six moved by a hair, four ended outright, and not one of them was a new question. Fifteen figures, a checked citation ladder, and the nineteen hours in which the artifact rewrote itself.open 01July 2026the-jacobian-conjectureThe Jacobian ConjectureFor eighty-seven years nobody could decide whether a polynomial map that never folds must be undoable. In July 2026 a language model wrote down a map that does not fold and still cannot be undone. This is what the question was, drawn from first principles, and why the answer is bigger than its critics think.open 02July 2026kimi-k3Kimi K3The first open model at three trillion parameters, read end to end from its config file and technical report: the three axes it scales along, how it was trained, what runs underneath it in production, what it scores, what it costs, and the short list of things Moonshot still has not said.open 03July 2026the-unit-distance-conjectureThe Unit Distance ConjectureIn May 2026 an unnamed model disproved a conjecture Erdős posed in 1946, using a theorem from 1964 that had been sitting on the shelf for want of an application. The interesting part is not that it was right. It is that three independent sources all explain why nobody else had bothered to look, and they agree.open 04July 2026the-jacobian-lensThe Jacobian LensAnthropic multiplied a language model's insides by a matrix and words came out: things the model was holding but had not said. The finding is real, the method is one derivative, and the two explanations that reached eight hundred thousand people are the two opposite ways to get it wrong. Here is the mechanism, built from scratch, plus my own measurements of what the instrument actually is.open 05July 2026the-two-button-calculatorThe Two-Button CalculatorIn March 2026 a Polish theoretical physicist showed that a single formula, exp(x) minus ln(y), generates every elementary function. It sat unnoticed for three weeks, then went everywhere at once, got a Wikipedia article, lost it three weeks after that, and almost nobody read the half of the paper that fails. Here is the construction built from scratch in your browser, the four separate places its arithmetic breaks, and my own ledger of the forty seven errors I made getting here, ten of which I created by fixing another one.open 06July 2026feiges-conjectureFeige's ConjectureFor twenty two years nobody could prove that a sum of honest, independent, wildly unpredictable quantities lands under its own mean plus one at least 1/e of the time. In July 2026 two teams proved it eleven hours apart, and both used the same sixty six year old theorem about where a flat cut through a shape's centre of mass lands. This is the puzzle from scratch, the volume that turned out to be hiding inside it, the machine that found the bridge, and my own account of why almost nobody noticed.open